CustomNumberSystem

With This You can flexibly generate strings also

Welcome to Customizable Number Systems world. You will able to customize your system characters. Easily make Transitions and Generate Numbers of any System. By the way, this library referres only to nonnegative integers.

NOTE: All objects in this library are immutable.

Ok, Lets See if it meets your requirements.

Usage

Lets create NumberSystem with digits ['a', 'b', 'c'], (power of each digit equal to its index in array):

const { NumberSystem } = require('custom-number-system')

const sys3 = new NumberSystem(['a', 'b', 'c'])

In this NumberSystem you can create numbers as big as you wish. e.g.

const num1 = sys3(1234)
const num2 = sys3('123456789123456789123456789123456789123456789')

Remember that whan you create numbers in current NumberSystem by providing number or string representation of number, they will be considered in decimal notation.

You can create number by providing valid powers array, where powers MUST be represented by numbers in range [0, system.base - 1].

const num = sys3([ 2, 2, 1, 0, 0 ])

Or you can simply convert number from one system to another:

const sys2 = new NumberSystem(['O', 'L'])

const num = sys2(8) // LOOO
const converted = num.toSystem(sys3) // converting...

You CANT create NumberSystem of base less than 2.

After you create numbers you can manipulate them as you wish.

const sys4 = new NumberSystem(['A', 'B', 'C', 'D'])
const num = sys4(8) // CA

const sys2 = new NumberSystem(['O', 'L'])
const operand = sys2(1) // L

// Result will be number in sys4 system.
const sum = num.add(operand) // CB
const sbtr = num.subtract(1) // A
const mul = num.multiply('1') // CA
const mod = num.remainder(operand) // A
const div = num.divide(1) // CA

Theres also increment and decrement methods at you serivce sir:

num.increment() // same as num.add(1)
num.decrement() // same as num.subtract(1)

NOTE:

1. If Result is negative when using arithmentical operations, undefined will be returned.
2. When using divide method, If divider equals to 0, undefined will be returned, else integer part of division will be taken as result (when result is negative, see case 1).
3. When using remainder method, if divider equals to 0, undefined will be returned, else NonNegative remainder will be taken as result (when result is negative, see case 1).

You can also compare numbers values with static methods of NumberSystem.

NumberSystem.lt(num1, num2) // less than
NumberSystem.le(num1, num2) // less than or equal
NumberSystem.gt(num1, num2) // greater than
NumberSystem.ge(num1, num2) // greater than or equal
NumberSystem.ne(num1, num2) // not equal
NumberSystem.e(num1, num2) // equal

You can get digit at appropriate index ( 0 based ) read from left.

const sys3 = new NumberSystem(['0', '1', '2'])

const num = sys3([2, 2, 1, 0, 0])

console.log(
    num[0].toString(), // 2
    num[1].toString(), // 2
    num[2].toString(), // 1
    num[3].toString(), // 0
    num[4].toString(), // 0
)

console.log(num[10]) // undefined

NOTE: For not existing digits undefined will be returned.

You can also use in operator to check if digit exists at given index:

// Continuation of above example.
console.log(
    1 in num // true

    -1 in num // false
    10 in num // false
)

You can also iterate through its digits with for in and for of loops, note that for of loop in this case is much more faster.

const sys3 = new NumberSystem(['0', '1', '2'])

const num = sys3([2, 2, 1, 0, 0])

for(const index in num) {
    console.log(num[index].toNumber())
}

for(const dig of num) {
    console.log(dig.toNumber())
}

// existing digit indexes
console.log(Object.keys(num)) // [ '0', '1', '2', '3', '4' ]
// existing digits
console.log(Object.values(num).map(dig => dig.toString())) // [ '2', '2', '1', '0', '0' ]

You can get generator of digits for current number:

const sys3 = new NumberSystem(['0', '1', '2'])

const num = sys3([2, 2, 1, 0, 0])

const start = 0
const end = num.length - 1
const step = 1

const digGen = num.digGenerator(start, end, step)
for(const dig of digGen) {
    console.log(dig.toNumber())
}
// Will be printed:
// 2
// 2
// 1
// 0
// 0

NOTE:

• You can omit end/step then they will be set to (num.length - 1)/1 appropriately.
• If start or end less than 0, then 0 will be used accordingly for start or end.
• If start or end more than num.length - 1, then num.length - 1 will be used accordingly for start or end.
• If step less or equal than 0 then 1 will be used as step.

You can get generator of numbers of NumberSystem instance.

const sys2 = new NumberSystem(['0', '1'])
const sys3 = new NumberSystem(['a', 'b', 'c'])

// start, end, step can be numbers of any system.
const start = sys2(10)
const end = sys3(100)
const step = sys2(1)

const numGen = sys3.numberGenerator(start, end, step)

for(const num3 of numGen) {
    console.log(num3.toString())
}

NOTE:

• If you omit end, generator will continue infinitely.
• If you omit step, it will be set to 1.
• If start or end less than 0, then 0 will be used accordingly for start or end.
• If step less or equal than 0 then 1 will be used as step.

You can get minimum or maximum numbers in rank:

const sys3 = new NumberSystem(['0', '1', '3'])

console.log(sys3.minInRank(3).toString()) // 100
console.log(sys3.maxInRank(3).toString()) // 333

NOTE:

• If rank is less than 1, then 1 will be used as rank.

Now note that Numbers are instances of only their constructor NumberSystemInstances, and NumberSystemInstances are instances of NumberSystem.

const sys2 = new NumberSystem(['0', '1'])
const num2 = sys2(1)

const sys3 = new NumberSystem(['a', 'b', 'c'])
const num3 = sys3(1)

console.log(num2 instanceof sys2) // true
console.log(num3 instanceof sys3) // true
console.log(num2 instanceof sys3) // false

console.log(sys2 instanceof NumberSystem) // true
console.log(sys3 instanceof NumberSystem) // true

You can check if some value is number instance.

const { NumberSystem } = require('custom-number-system')

const sys = new NumberSystem(['0', '1'])
const num = sys2(1)

console.log(NumberSystem.isNumber(num)) // true
console.log(NumberSystem.isNumber(1)) // false

Advanced

You can use instead of digits array, an object that implements IDigitsConfig:

interface IDigitsConfig {
    base: number,
    readonly maxBase: number
    digGen: (this: IDigitsConfig, ...powers: number[]) => (string | undefined)[],
    readonly dinamicArity?: boolean,
}

Here digGen method binded to current object. It's must guarantee that it will return digit for all powers from 0 to maxBase.

The only modifiable property is base. You can change base between 2 and maxBase, when you pass config to NumberSystem constructor, base will be fixed, and only digits in range [0, base] will be used.

Interface also define that powers not in range [0, maxBase] must return undefineds.

dinamicArity defines if you can pass multiple powers to digGen.

NOTE: digGen always return an array of digits.

Example 1 is CharGroup constructor which will give you digitsConfig of visible characters:

const { CharGroup } = require('custom-number-system')

const charGroup = CharGroup('ab$cd🌐')

console.log(
    charGroup.maxBase,
    charGroup.digGen(-1, 0,1,2,3,4,5,6)
)
// Will be printed:
// 6, [ undefined, 'a', 'b', '$', 'c', 'd', '🌐', undefined ]

Example 2 is digitsConfigMixer utility function:

const { digitsConfigMixer } = require('custom-number-system')

const digitsConfig = digitsConfigMixer([97,122], ['A', 'Z'], 'Blablabla', 97, CharGroup('ab$cde🌐'))

This digitsConfig includes(starting from power 0) symbols:

• [97, 122]: from 'a' to 'z'
• ['A', 'Z']: then from 'A' to 'Z'
• 'Blablabla': word 'Blablabla'
• 97: symbol 'a'
• CharGroup('ab$cde🌐'): symbols 'a', 'b', '$', 'c', 'd', '🌐'

And you can check if object correctly implements IDigitsConfig interface:

const { isDigitsConfig } = require('custom-number-system')

console.log(isDigitsConfig(digitsConfig)) // true

All this can also be found in TsDocs.